Not all black sheep were convicts, it was very common to send remittance men and women often with their families overseas to get them away from the area where they had disgraced themselves.

A place of residence was bought and regular sums of money deposited in the bank to keep them away. Administration of this was generally arranged with a firm of lawyers, who perhaps kept a friendly or fatherly eye on them.

The reason they were banished could be because they had drug or alcohol or gambling problems.
Health Reasons.
Career not approved of by family.
Married outside their station in life.
Married outside their race.
Some family land dispute.
Possibly for some reason I haven't even thought of an embarrassment to a family who could afford the out of sight out of mind policy and pay for it.